Cambridge Additional Mathematics

Logarithms (Chapter 5) 137

EXERCISE 5C

1 Write as a single logarithm or as an integer:

a lg 8 + lg 2 b lg 4 + lg 5 c lg 40¡lg 5

d lgp¡lgm e log 48 ¡log 42 f lg 5 + lg(0:4)

g lg 2 + lg 3 + lg 4 h 1 + log 23 i lg 4¡ 1

j lg 5 + lg 4¡lg 2 k 2 + lg 2 l t+lgw

m logm 40 ¡ 2 n log 36 ¡log 32 ¡log 33 o lg 50¡ 4

p 3 ¡log 550 q log 5100 ¡log 54 r lg

¡ 4

3

¢

+lg3+lg7

2 Write as a single logarithm or integer:

a 5lg2+lg3 b 2 lg 3 + 3 lg 2 c 3lg4¡lg 8

d 2 log 35 ¡3 log 32 e^12 log 6 4 + log 63 f^13 lg

¡ 1

8

¢

g 3 ¡lg 2¡2lg5 h 1 ¡3lg2+lg20 i 2 ¡^12 logn 4 ¡logn 5

3 Simplify without using a calculator:

a

lg 4

lg 2

b

log 527

log 59

c

lg 8

lg 2

d

lg 3

lg 9

e

log 325

log 3 (0:2)

f

log 48

log 4 (0:25)

Check your answers using a calculator.

Example 9 Self Tutor

Show that:

a lg

¡ 1

9

¢

=¡2lg3 b lg 500 = 3¡lg 2

a lg

¡ 1

9

¢

=lg(3¡^2 )

=¡2lg3

b lg 500

=lg

¡ 1000

2

¢

= lg 1000¡lg 2

=lg10^3 ¡lg 2

=3¡lg 2

4 Show that:

a lg 9 = 2 lg 3 b lg

p

2=^12 lg 2 c lg

¡ 1

8

¢

=¡3lg2

d lg

¡ 1

5

¢

=¡lg 5 e lg 5 = 1¡lg 2 f lg 5000 = 4¡lg 2

g log 6 4 + log 6 9=2 h log 153 ¡log 15 45 =¡ 1 i 2 log 12 2+^12 log 12 9=1

5 Find the exact value of:

a 3 lg 2 + 2 lg 5¡^12 lg 4 b 2 log 23 ¡log 26 ¡^12 log 29

c 5 log 6 2 + 2 log 63 ¡^12 log 616 ¡log 612

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_05\137CamAdd_05.cdr Tuesday, 21 January 2014 2:47:44 PM BRIAN